Consider two groups with n₁ , n₂ observations in each group, and let N=n₁+n₂ We assume that

y_i=?₁+?_ifori=1,2 ,... , n₁ and that

y_i=?₂+?_ifori=n₁+1,... , N ,

where ?i ~ N ( 0, ?²)

Show that the least squares estimator for u , u, are n yi nji=1 N 1 2 = E yi ni=n+1